Research on normal and power law distributions
From Evo Devo Universe
Can we make the case that a top down (developmental) process commonly creates a normal distribution and a bottom up (evolutionary) process commonly creates a power law distribution?
In George K. Zipf's Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology, 1949, he credits the observed power law for word usage as due to "the economy of the evolutionary process," or what we might call creativity operating within matter, energy, space, and time (MEST) resource efficiency constraints. Humans learning how to use language, and humans inventing new ways to use any still-growing language both seem Zipfian.
Physicists Dietrich Stauffer and Christian Schulze have developed a model (Monte Carlo simulation of the rise and the fall of languages) of how languages evolve. They find the size distribution of languages is log-normal (follows a power law) under high mutation rates (evolutionary innovation), but under low mutation rates (developmental optimum?), one language dominates.
Ramon Ferrer i Cancho and Ricard V. Sole, in Least effort and the origins of scaling in human language, 2003, PNAS 100(3)789-791, states that Zipf's principle of least effort hypothesis (for speaker and hearer) still applies to word usage in all languages. Is language usually an evolutionary system? It seems so. Under what special circumstances (low innovation? closed grammars? limited lexicons?) can we observe it transition to a developmental one, and can we then observe normal-like aggregation around the optima at that point, as we might intuitively expect?
Peter Winiwarter proposes many examples of ZPM distributions here. Peter G. Neumann says here that Vitold Belevitch showed that such distributions are all mathematically related, by Taylor series expansions (with first, second, third order truncations). Belevitch's paper is: On the Statistical Laws of Linguistic Distribution, Annales de la Societe Scientifique de Bruxelles 73(III)1959,310-326. Can someone find and link to a PDF of this paper? What does this imply about transition dynamics?
Lada Adamic and Bernardo Huberman, Zipf's law and the Internet, Glottometrics 3,2002,143-150. An observation that Zipf's law governs many emergent features of the internet, a system that seems much more evolutionary (in its early stage of creation today) than developmental.
An interesting paper] by Ronald E. Wyllys, Empirical and Theoretical Bases of Zipf's Law. It quotes Herbert Simon as saying the reason the Zipf distribution is ubiquitous must have something to do with "shared probability processes" between all these otherwise different phenomena. What processes? Evo, devo, or computation perhaps?